Embed Size (px)
Citation preview
Mrs. Jo Marks
Maths Leader & Lower
School Phase Leader
*Calculation
Methods
Denmead Junior School
*Key ideas for DJS
*One more, one less
*Doubling and halving
*Part/whole
*Patterning
*Positioning a number (on the number
line) helps inform the right decision for
calculation
*
A pupil really understands a mathematical
concept, idea or technique if they can:
*describe it in their own words;
*represent it in a variety of ways
*explain it to someone else
*create examples and non-examples;
*see connections with other facts and ideas;
*recognise it in new situations and contexts;
*make use of it in various ways, including new
situations.
Addition
Addition
Unstructured number line
Addition
48
50
78 80 84
48 84
8 10 15
+2
+30 +2
+5
+4
+2 +3
4
8 + 7 = 15
48 + 36 = 84
or:
Partitioning
47 40 7
76 70 6
110 13 123
Addition
Expanded column method
47
76
13
110
123
Addition
Compact column method
1 1
47
76
123
1 1
258
87
345
1 1
366
458
824
Addition
Subtraction
Counting back(taking away from largest to smallest)
Subtraction
Subtraction
Structured number line
Unstructured number line
Subtraction
Counting on (adding)
Subtraction
Subtraction
Expanded column method— no ‘taking’
500 60 3
200 40 1
300 20 2
Subtraction
Expanded column with ‘taking’400
500 60 3 400 160 3 500 160
604
3 5 616
3
200 70 1 200 70 1 200 70 1 2 71
200 90 2 200 90 2 2 9 2
400
500 60 3 400 160 3 500 160
604
3 5 616
3
200 70 1 200 70 1 200 70 1 2 71
200 90 2 200 90 2 2 9 2
500
500 60 3 400 150 13 500
40050
60
15013
3
134
5 615 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 80 5 200 80 5 2 8 5
500
500 60 3 400 150 13 500
40050
60
15013
3
134
5 615 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 80 5 200 80 5 2 8 5
Subtraction
Expanded column with ‘taking’
400
500 0 3 400 90 13 500
400100
0
903
3
134
5 09 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 20 5 200 20 5 2 2 5
400
500 0 3 400 90 13 500
400100
0
903
3
134
5 09 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 20 5 200 20 5 2 2 5
Subtraction
Compact column
400
500 60 3 400 160 3 500 160
604
3 5 616
3
200 70 1 200 70 1 200 70 1 2 71
200 90 2 200 90 2 2 9 2
500
500 60 3 400 150 13 500
40050
60
15013
3
134
5 615 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 80 5 200 80 5 2 8 5
400
500 0 3 400 90 13 500
400100
0
903
3
134
5 09 13
3
200 70 8 200 70 8 200 70 8 2 7 8
200 20 5 200 20 5 2 2 5
Multiplication
Multiplication as repeated addition
2 + 2 + 2 + 2 = 8
4 x 2 = 8
2 multiplied by 4
4 lots of 2
Multiplication
Multiplication
Repeated addition on a number line
0 5 10 15 20
+
5
+
5
+
5
+
5
Multiplication
Know multiplication tables - up to 12x12
Understand multiplication as an array
Multiplication
Grid method
23 x 8 = 184160 + 23 = 184
500 150
+ 30 680
23 x 8
136 x 5
Multiplication
Short multiplication—only if the multiplier is a ‘one’E.g. 24 x 6 or 342 x 7 or 2741 x 6(Year 5 and Year 6)
Multiplication
Grid method
70 8
160
403505
20 1400
1560
3901950
+
78 x 25
X
Multiplication
Long multiplication—when the multiplier is a 2 or 3 digit number(Year 5 and Year 6)
Division
Division
Grouping
How many groups of 4 can be made with 12? 3
Division
Sharing
Division
Division using arrays
Pupils should also show that the same array can represent 12 ÷ 4 = 3 if grouped horizontally.
Division
Chunking on a number line
Division
Adding on or taking away
45 9 = 5
0 18 36 459 27
+9 +9 +9 +9 +9
How many lots of 9 makes 45?
Division
0 40 80 96
10 x 4 10 x 4 4 x 4
40 40 16
How many lots of 4 altogether?10 + 10 + 4 = 24
Division by chunking on a number line
Make sure the number you multiply by goes in the same position each time
96 4 = 24
Division
Division
DivisionWhat does the remainder
mean? How should it be
represented?
…..as a fraction or as
a decimal
Division
Can I do this in my head? How big will my
answer be? (approximation)
Could I use jottings to keep track of the
calculation?
Do I need to use an expanded or compact
method?
Did I check my answer?
Inverse check
Against my approximation
Using another method
Love maths!
Number bonds and Times tables
Telling the time
Measurements
*Ways to support your child
* 1, 10, 5 strategy for calculating multiplication facts
*
